Question: How much would a thimbleful of a neutron star weigh out of interest?

It depends on which part of the neutron star you were weighting. Assuming that a thimblefull is about one cubic centimeter, then with the density of the crust of a neutron star, it would weight about a tonne. However, if we were to take the core of the neutron star, it would be a lot heavier, around 100 billion tonnes, which is about the weight of 1000 mount everests.